OLYMPIAD > FUNCTIONS
Functions used in explaining symmetry.
Functions are the foundation of mathematics algebra. In your years in junior and high school, you will surely see your fair share of functions, be it differentiating or graph sketching, trigonometry or polynomials. Yet in most cases, the function used forms a piece of explaining a particular concept.
In this chapter, we shall investigate the functions themselves. We all know what a function does: "Put in a value and get another value". Yet, not many of us know the inner workings or various manipulations involve with functions. There's a lot more than domain and range.
A note to the student. I consider functions one of the more difficult problems in the olympiad. It addresses the crux of problem solving by way of not having a clear path to a solution. The AMC12 has seen a recent increase in the problems involving functions. Those participating in AMC10 will see no function questions.
Joesph Fourier
Inverse
Bijections
Brownian Motion
Graph sketching
Group theory
Satistics
Functions used in explaining symmetry.
In this chapter, we shall investigate the functions themselves. We all know what a function does: "Put in a value and get another value". Yet, not many of us know the inner workings or various manipulations involve with functions. There's a lot more than domain and range.
A note to the student. I consider functions one of the more difficult problems in the olympiad. It addresses the crux of problem solving by way of not having a clear path to a solution. The AMC12 has seen a recent increase in the problems involving functions. Those participating in AMC10 will see no function questions.
CONCEPT CONTENTS
> INTRODUCTION TO FUNCTIONS
> DOMAIN AND RANGE OF A FUNCTION
> SKETCHING A COMPLICATED FUNCTION
> GENERAL EQUATION OF A CIRCLE
AMC QUESTIONS
> 1991 ASHME #21
> 1993 AMC12 #26
> 1993 AHSME #12
> 1996 AHSME #12 (INTERESTING)
> 1996 AHSME #25 (DIFFICULT)
> 1980 AHSME #14
Notable Mathematicians
Leonhard EulerJoesph Fourier
Important Theorems
Domain and Range Inverse
Bijections
Brownian Motion
Applications
TrigonometryGraph sketching
Group theory
Satistics
